Turkyilmazoglu Mustafa
Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara Turkey.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
Eur Phys J Spec Top. 2022;231(18-20):3591-3601. doi: 10.1140/epjs/s11734-022-00614-6. Epub 2022 May 30.
A simplistic reaction-diffusion model is undertaken in the present work to mathematically explore the spatio-temporal development of concentration of indoor aerosols containing infectious COVID-19 respiratory virus nuclei. Extracting exact solutions of concentration field under the influence of several physical parameters is preferred rather than adopting a more realistic complex model requiring time-consuming numerical simulations. Even though the proposed model is not sophisticated, the analytical solutions can provide quick prediction of the probability of contracting the virus in a ventilated closed room. Moreover, from the obtained elementary solutions of the viral concentration field, it is easy to analyze its spatio-temporal evolution and final equilibrium state. Formulae enable us to estimate the time to get infected and the risk of getting infected within an elapsed time under various physical operative situations involving a uniform infectious particle mixture ejection into the medium, wearing a face mask with a well-defined efficiency parameter and taking into account a localized source of infection. One of the essential conclusion from the current research is that less aerosols carrying COVID-19 particles are as a result of good indoor ventilation conditions, of removing the medium air through windows (or other exits) and of wearing masks of high efficiency. Moreover, the risk and probability of being caught by the indoor COVID-19 disease increases in time, particularly in the downstream of a localized infectious person. The results can be beneficial to understand and take necessary safety considerations against the infection risk in closed public or governmental environments.
在本研究中采用了一个简单的反应扩散模型，以数学方式探究含有传染性新冠病毒呼吸道病毒核的室内气溶胶浓度的时空发展情况。相比于采用需要耗时数值模拟的更现实复杂模型，提取在几个物理参数影响下浓度场的精确解更为可取。尽管所提出的模型并不复杂，但解析解能够快速预测在通风良好的封闭房间内感染病毒的概率。此外，从所获得的病毒浓度场基本解中，很容易分析其时空演变以及最终平衡状态。公式使我们能够估计在各种物理操作情况下被感染的时间以及在经过一段时间内被感染的风险，这些情况包括向介质中均匀喷射传染性颗粒混合物、佩戴具有明确效率参数的口罩以及考虑局部感染源。当前研究的一个重要结论是，良好的室内通风条件、通过窗户（或其他出口）排出室内空气以及佩戴高效口罩，会减少携带新冠病毒颗粒的气溶胶。此外，感染室内新冠疾病的风险和概率会随时间增加，特别是在局部感染源下游。这些结果有助于理解并针对封闭公共或政府环境中的感染风险采取必要的安全措施。
